Say what multicollinearity is and what it does to a regression analysis

Multicollinearity arises when two or more independent variables are highly correlated with each other. The coefficients stay unbiased, but their standard errors swell, so individual t-statistics look insignificant even though the model as a whole fits well. The classic sign is a high R² and significant F-test with few or no significant t-statistics. Pairwise correlations can miss it when three or more variables combine. Measure it with the variance inflation factor for each variable, VIF = 1 ÷ (1 − R²), where R² comes from regressing that variable on the others. Above 5 needs investigation, above 10 is serious, as rules of thumb rather than tests. Remedies are dropping or combining variables, a different proxy, or more data.